Answer
a. $H_{o}: p = 32$
$H_{1}: p < 32$
b. Type-I Error: Sample evidence leads consumer advocate to believe that a certain peanut butter manufacturer is shorting customers by underfilling the jars. However, in fact the jars do contain 32 ounces of peanut butter.
c. Type-II Error: Sample evidence leads consumer advocate to believe that a certain peanut butter manufacturer is filling at least 32 ounces of peanut butter. However, in fact the jars contain less than 32 ounces of peanut butter.
Work Step by Step
a. Null hypothesis (the jars have 32 oz of peanut butter):
$H_{o}: p = 32$
Alternative hypothesis (the jars have less than 32 oz of peanut butter):
$H_{1}: p < 32$
b. Type-I Error: Sample evidence leads consumer advocate to believe that a certain peanut butter manufacturer is shorting customers by underfilling the jars. However, in fact the jars do contain 32 ounces of peanut butter. In other words, the scientists have rejected the null hypothesis ($H_o$), but it in fact is true.
c. Type-II Error: Sample evidence leads consumer advocate to believe that a certain peanut butter manufacturer is filling at least 32 ounces of peanut butter. However, in fact the jars contain less than 32 ounces of peanut butter. In other words, the scientists have not rejected the null hypothesis ($H_o$), when in fact the alternative hypothesis ($H_1$) is true.
